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My principle aim in the original Hedrick lectures, as well as in this enlarged version was to show that (a) extremely simple observations are often the starting point of rich and fruitful theories and - PowerPoint PPT Presentation
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My principle aim in the original Hedrick lectures, as well as in this enlarged version was to show that (a) extremely simple observations are often the starting point of rich and fruitful theories and (b) many seemingly unrelated developments are in reality variations on the same simple theme.
A theoretician working on glass
Courtesy Roald Hoffmann
The Theory of Glasses
I. Experimental phenomenology of glass
II. Energy landscapes & random first order transitions
• T.R. Kirkpatrick, D. Thirumalai, R. Hall, Y. Singh, J.P. Stoessel, and P.G. Wolynes
III. The mosaic picture of random first order transitions
• X.Y. Xia, V. Lubchenko, J. Stevenson, J. Schmalian
IV. Quantum theory of glasses• V. Lubchenko
Dynamics and thermodynamics near the glass transition
Ediger, Angell & Nagel, JPC 1996
Super Arrhenius temperature dependence of rates
“strong”
“fragile”
14 o
rder
s of
m
agni
tude
0
0
0TT
DT
e Vogel-Fulcher Law
SiO2
OTPglycerol
The glass transition and the “Kauzmann Paradox”
ΔCP
Slower cooling leads to sharper change
ΔCP is larger for “fragile” liquids
Ediger, Angell & Nagel, JPC 1996
The 3rd law (?)
T
T
Pref
ref
dTT
CSS
T0Kauz = T0
VF (±10°K)!!!
Residual entropy diminishes with slower cooling
1/Tm 1/T0 1/T
Latent heat/Tm
1/Tg
Sliquid -Scrystal
Aging: dynamics continues, but slower, in the glassy state
Alegria et al. Macromolecules,
1998
V. Lubchenko & PGW, JCP (2004)
T
Ex
T
Ex
ge
)1(
0
“Non-linearity parameter” 0<x<1
Slow quench
Fast quench
Narayanaswamy, Tool, Moynihan
Glasses have more low energy excitations than crystals
Raychaudhuri and Pohl, PRB 1982
Stephens, PRB, 1973
Entropy of these excitations is still small
aTdTT
CS
TV 0"" Extrapolated to
300°K, this is ≈10-2kB
CV/T
Intercept
CV =aT+AdebyeT3
The “Standard Model” of Quantised amorphous solids
dxC
gH ii
i
i
22
2 1
2/0
02/
2/
2/
ddPddP )/log,( max
Two-level tunneling states
tunneling Strain int’n
Continuum phonons
~Assume a distribution of ε, Δ
Surprisingly small variation of (reflected in CV) P
W. Phillips, P.W. Anderson, Halprin, Varma
The Architecture of Aperiodic Crystals
Model handbuilt by J.D. Bernal
RFOT theory predicts dynamic fragility from thermodynamics
0
0
0TT
DT
e
LJm
m
PP
ST
HmoleC
C1
)(
cTS
rF 0
203
PC
RD
32
20
20
2
20
0
25.1
/log
4
3
r
Tk
e
ra
r
Tk
B
B
Dm=590/(m-16)Bohmer, Ngai, & Angell, JCP, (1993)
RFOT theory predicts fragility parameter, m
m from RFOT
m from experiment
RFOT predicts the non-exponentiality parameter from fragility and
thermodynamics
ξ
Mosaic picture
ξ=4.5a
RFOT predictions of CRR size agree with experiment
22
4 TP
B
C
Tk
Berthier et al. Science (2005) 310, 1797
Data from:
Bohmer et al. J. Chem. Phys. (1993) 99, 4201
3/122
2
2)10ln(/
P
B
C
km
ea
Berthier et al. inequality
34 )/( a
Shapes of CRR’s
• Surface interaction energy wants compact shape
• Shape entropy wants fractal shape
),(log),( 0int bNTkbvNTSbNF Bc
Small surface area
Large surface area
Gebremichael et al. J. Chem. Phys 120, 4415
Percolation clusters and strings
• The surface of percolation clusters and strings scales with volume: b=αN.
)28.1()( Bc kSTNNF ),(log),( 0
int bNTkbvNTSbNF Bc
)13.1()( Bc kSTNNF
Percolation:
Strings:
Shape transition signals crossover temperature
Same as Hagedorn transition in string theory!
String Transition
Mode Coupling Transition
Sc(Tg)/Sc
Log(
Vis
cosi
ty ,
P)
Non-equilibrium aging effect is predicted from fragility within RFOT theory
After long-aging the mosaic is more heterogeneous
“Ultra-slow” relaxations
Local libraries lead to tunneling resonancesLubchenko & PGW
N*
ΔE=0
Density of ResonancesgT
g
eT
n /
3
1)(
31453
101
)( mJT
Png
ε<<Tg
Direct spectroscopic evidence of complex structure of 2LS
THE DEEPEST AND MOST INTERESTING UNSOLVED problem in solid state theory is probably the theory of the nature of glass and the glass transition. This could be the next breakthrough in the coming decade The solution of the problem of spin glass in the late 1970s had broad implications in unexpected fields like neural networks, computer algorithms, evolution, and computational complexity. The solution of the more important and puzzling glass problem may also have a substantial intellectual spin-off. Whether it will help make better glass is questionable.
P. W. AndersonJoseph Henry Laboratories of Physics
Princeton UniversityScience, 1995